Field of the Invention
The invention relates to security systems in automobiles, and more specifically to a transmitter unit for an anti-theft system of a motor vehicle and to methods for operating the transmitter unit, in which signals in the transmitter unit are transmitted on a carrier signal.
With a periodic rectangular signal u.sub.R (t) (FIG. 4) as the carrier oscillation it is possible to transmit data or energy by a transmission antenna in wireless fashion without major power losses. Each periodic rectangular signal u.sub.R can be broken down in a known manner with the aid of Fourier analysis--as shown in FIG. 4--into a sum of partial oscillations u.sub.i (where i=1 to n). As the partial oscillations, the results are a fundamental oscillation u.sub.1 and many harmonic oscillations u.sub.3 through u.sub.9 (in FIG. 4, for the sake of simplicity, only the partial oscillations u.sub.i up to the ninth order are shown). The amplitudes of the individual partial oscillations u.sub.i depend on the shape of the rectangular signal u.sub.R.
The sum of the fundamental oscillation u.sub.1 and all the harmonic oscillations ##EQU1## with n=9) then produces the rectangular signal u.sub.R with its amplitude u (the rectangular signal u.sub.R is periodic, with a period length T=2.pi.: it assumes the value +u from 0 to .pi. and the value -u from .pi. to 2.pi.).
According to Fourier, every time function u(t) for every periodic non-sine-shaped oscillation can be expressed as an infinite series: ##EQU2## where u(t)=time function, a.sub.o, a.sub.n, and b.sub.n =Fourier coefficients, n=integer, .omega.=2.pi./T=angular velocity, T=period length, and t=time.
In each Fourier analysis, the Fourier coefficients a.sub.o, a.sub.n and b.sub.n must be calculated: ##EQU3##
If the rectangular signal of FIG. 4 is broken down in the Fourier transform, the result using equations (1) through (3) is: ##EQU4##
This shows that the fundamental oscillation u.sub.1 is a sine-wave oscillation with the amplitude 4u/.pi., while the third harmonic oscillation u.sub.3 oscillates in sine-wave fashion with triple the frequency (3 .omega.t), and the amplitude is one third the amplitude of the fundamental oscillation u.sub.1.
In this rectangular signal u.sub.R, there are no even-numbered orders of harmonic oscillations. The frequency of the fundamental oscillation u.sub.1 is identical to the frequency of the rectangular signal. The harmonic oscillations u.sub.i have integral multiples of the fundamental frequency.
For wireless data or energy transmission in the automotive field, the rectangular signals can be used as a carrier oscillation, and information can be modulated onto them. For such transmissions, very specific frequency bands are authorized for the carrier oscillation. If a rectangular signal is used as a carrier oscillation, then the fundamental oscillation u.sub.1 is within an authorized frequency band. The third harmonic oscillation u.sub.3 (which for the rectangular signal u.sub.R has the highest amplitude of all the harmonic oscillations) may have its frequency in an unauthorized frequency range. As a result, the signal transmission can interfere with other applications outside the motor vehicle.